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- W2169189571 abstract "The purpose of this paper is to understand the geometric structure of the $L^2$-Wasserstein space $pp$ over the Euclidean space.For this sake, we focus on its cone structure.One of our main results is that the $L^2$-Wasserstein space over a Polish space has a cone structure if and only if so does the underlying space.In particular, $pp$ turns out to have a cone structure.It is also shown that $pp$ splits $R^d$ isometrically but not $R^{d+1}$." @default.
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- W2169189571 date "2008-12-15" @default.
- W2169189571 modified "2023-09-27" @default.
- W2169189571 title "Cone structure of $L^2$-Wasserstein spaces" @default.
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